Questions: -3x - 3 < -x - 5

Transcript text: -3 x-3<-x-5

Solution

Solution Steps

To solve the inequality \(-3x - 3 < -x - 5\), we need to isolate \(x\) on one side of the inequality. We will first add \(3x\) to both sides, then add \(5\) to both sides, and finally divide by the coefficient of \(x\) to solve for \(x\). Once we have the solution, we will express it in interval notation.

Step 1: Simplify the Inequality

First, we start by simplifying the given inequality: \[ -3x - 3 < -x - 5 \]

Step 2: Move All Terms Involving \( x \) to One Side

Add \( 3x \) to both sides of the inequality to move all terms involving \( x \) to one side: \[ -3x + 3x - 3 < -x + 3x - 5 \] This simplifies to: \[ -3 < 2x - 5 \]

Step 3: Isolate the Term Involving \( x \)

Next, add 5 to both sides to isolate the term involving \( x \): \[ -3 + 5 < 2x - 5 + 5 \] This simplifies to: \[ 2 < 2x \]

Step 4: Solve for \( x \)

Divide both sides by 2 to solve for \( x \): \[ \frac{2}{2} < \frac{2x}{2} \] This simplifies to: \[ 1 < x \] or equivalently: \[ x > 1 \]